The present invention relates to a method of stably controlling a snake motion phenomenon of a to-be-rolled material which occurs in a step of rolling a long sheet metal in a rolling mill, and also to a controlling apparatus for stabilizing behavior of the rolled material in the rolling mill.
FIG. 12 shows a rolling system of the prior art to which the invention is to be directed. In the figure, 1 denotes a to-be-rolled material, 2a and 2b denote work rolls, 3a and 3b denote back-up rolls, 4a and 4b denote pressure sensors, 5 denotes the geometric center of a rolling mill, 6 denotes the geometric center of the to-be-rolled material, 8a and 8b denote draft devices, 9a and 9b denote load signals, 10a and 10b denote leveling signals, and 11 denotes a control device.
During a rolling process, a snake motion phenomenon in which the to-be-rolled material abruptly moves in the width direction is caused by mechanical characteristics of the rolling mill, lateral asymmetry in shape of the to-be-rolled material, a difference between rolling speeds of the left and right sides, and the like. When such a snake motion once occurs, rolling rolls are damaged so that the accuracy of a product is lowered, or the to-be-rolled material collides against the rolling mill so that the rolling process is disabled, thereby lowering the productivity.
Conventionally, a snake motion is prevented from occurring by conducting a rolling process with a crown so that rolling edge portions of a to-be-rolled material are thinner than the center portion. However, there is a tendency to reduce the degree of a crown so as to comply with the increasing demand for the higher accuracy of the thickness. Therefore, a situation inevitably arises in which a snake motion easily occurs.
As a technique of controlling a snake motion, disclosed are methods such as that in which the control device 11 indirectly detects the amount of a snake motion by means of the load signals and a snake motion control is conducted on the basis of the detected value corresponding to the amount of the snake motion, and that in which a snake motion sensor disposed in the inlet side of a rolling mill directly detects a snake motion and a snake motion control is conducted on the basis of the detected amount of the snake motion. In both methods, a proportional control, a proportional differential control, or the like is applied. Japanese Patent Publication (Kokai) No. 8-323412 discloses a control system in which the amount of a snake motion and a differential value of the amount are handled as state variables and a state feedback control is conducted by using a state variable that is estimated by an observer.
In the method in which the load signals are detected, a technique in which a proportional differential control is applied seems to cause the whole control system to become unstable. When this technique is applied to an actual rolling mill, however, the draft device functions as a delay system. As a result, the whole of the system is prevented from becoming unstable. However, the time constant of the delay system depends on the draft device, and it is difficult to arbitrarily design the time constant as a design factor of the control system. Furthermore, there is a problem in that, depending on the value of the time constant, the time constant cannot be used in stabilization of the whole system.
The above phenomenon will be described in detail. Assuming that a snake motion phenomenon and characteristics of a rolling mill affecting the snake motion phenomenon are included in a controlled object, operation characteristics of the controlled object are represented by expression (1) . EQU y.sub.c ={ay.sub.c +b(d.sub.s +.delta.S)+h.sub.1 .delta.H}/s.sup.2 +y.sub.c 0 EQU .delta.P=cy.sub.c -d(d.sub.s +.delta.S)+h.sub.2 .delta.H (1)
where yc means the amount of a snake motion, yc0 means the initial amount of the snake motion, .delta.S means a lateral deviation of leveling, .delta.H means a wedge amount (a difference in thickness between the left and right sides of the to-be-rolled material) on the inlet side, .delta.P means a lateral deviation of loads, and a, b, c, d, h1, and h2 are constants depending on the rolling mill, rolling conditions, etc.
When expression (1) is indicated in the form of a transfer function from the input .delta.S to the output .delta.P, expression (2) below is obtained. FIG. 2 shows frequency characteristics of expression (2). ##EQU1##
In the controlled object, there exist an unstable pole and an unstable zero point. Therefore, the system is very unstable and hence it is difficult to control the system. Specifically, when the gain is lower than 0 [dB] in the low-frequency region, or when the gain is higher than 0 [dB] in the high-frequency region, the system becomes unstable.
In FIG. 3, (a) shows frequency characteristics of an open-loop transfer function in the case where a proportional differential control is applied to the controlled object. When the control device is configured by only a proportional differential control, the system can be stabilized in the low-frequency region by adequately setting the proportional gain as shown in (a) of FIG. 3. By contrast, in the high-frequency region, the gain is affected by the differential gain so as to be infinity and hence the whole system inevitably becomes unstable. In (b) and (c) of the frequency characteristic diagram of FIG. 3 in which a proportional differential control is applied and the draft device is approximated by a delay system (in FIG. 3, a first order delay system), the gain in the high-frequency region is not infinity but constant, because of the characteristics of the delay system.
In the case where the draft device quickly responds, however, the gain characteristics in the high-frequency region exceeds 0 [dB] as shown in (b) of FIG. 3, and hence the system is unstable. Even in the case where the draft device has an adequate time constant as shown in (c) of FIG. 3, sufficient robust stability cannot be considered. In the design of a control gain mentioned in documents distributed in Thirty-first joint lecture on plastic working, "Study on a snake motion control in hot strip rolling," a stable range of a control gain is described, but a clear design method is not described. Furthermore, also robust stability is not described.